arxiv: 2412.06264 · v1 · submitted 2024-12-09 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Flow Matching Guide and Code

Yaron Lipman , Marton Havasi , Peter Holderrieth , Neta Shaul , Matt Le , Brian Karrer , Ricky T. Q. Chen , David Lopez-Paz

show 2 more authors

Heli Ben-Hamu Itai Gat

Authors on Pith no claims yet

Pith reviewed 2026-05-12 10:22 UTC · model grok-4.3

classification 💻 cs.LG

keywords flow matchinggenerative modelingdiffusion modelsmachine learningpytorchimage generationvideo generationaudio synthesis

0 comments

The pith

Flow Matching is a generative modeling framework that has achieved state-of-the-art performance across images, video, audio, speech, and biological structures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper delivers a self-contained review of Flow Matching as a framework for generative modeling. It walks through the mathematical foundations, important design choices, and available extensions while supplying a PyTorch package with concrete examples for image and text generation. A sympathetic reader would care because the approach offers a unified way to produce high-quality samples from complex data distributions in many different fields. If the review holds, it lowers the barrier for researchers to implement and improve upon these models without starting from scattered sources.

Core claim

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples, this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

What carries the argument

The Flow Matching framework, which learns a velocity field to transport samples continuously from a source distribution to a target data distribution.

If this is right

Researchers can use the released code to implement Flow Matching directly for image and text generation tasks.
The reviewed design choices allow systematic selection of paths and conditioning methods for new applications.
Extensions discussed can be combined to improve sample quality or training efficiency in specialized domains such as biology.
The guide provides a single reference that reduces the need to consult multiple scattered papers when starting new projects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Making the code public may speed up adoption by allowing direct testing and modification of the velocity-field approach in new settings.
The framework's reported success across unrelated data types suggests it could serve as a base for multimodal models that generate combined text and image outputs.
If the velocity-field view proves more stable than score-based alternatives, future work might focus on scaling these models to higher resolutions without additional architectural changes.

Load-bearing premise

The review accurately and completely summarizes the mathematical foundations, design choices, and extensions of Flow Matching without errors or omissions.

What would settle it

Reproducing the PyTorch examples on standard benchmarks and finding that performance falls short of the claimed state-of-the-art levels in one of the listed domains.

read the original abstract

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a practical guide and code release for Flow Matching that aggregates existing work without new results.

read the letter

This paper is basically a how-to guide for Flow Matching, complete with PyTorch code and examples for things like image and text generation. The authors pull together the math foundations, design choices, and some extensions from existing work. It's positioned as a resource for both new and experienced folks in the area. What stands out is the effort to make it self-contained and accessible, with runnable examples. That could save people time when trying to apply Flow Matching in their own projects. The code release is a plus if it works as advertised and covers the key cases. On the downside, since it's a review, there's no new math or experiments to check. The claim about state-of-the-art performance comes from prior papers, so readers will need to look there for the evidence. I didn't spot any obvious errors in the abstract, but the full accuracy of the summaries would need checking against the original sources. Also, as with any code release, the long-term maintenance isn't guaranteed. This is for researchers or engineers who want a practical entry point into Flow Matching without digging through multiple papers. It might be worth a serious look if you're in generative modeling and need the code to build on. I'd recommend sending it for peer review, mainly to verify the code and explanations are correct and complete. It could serve as a good reference point for the community.

Referee Report

0 major / 2 minor

Summary. The manuscript presents 'Flow Matching Guide and Code,' a self-contained review of the Flow Matching (FM) framework for generative modeling. It covers the mathematical foundations, key design choices, and extensions of FM, while releasing a PyTorch package that includes runnable examples for tasks such as image and text generation. The work positions itself as a practical resource for both novice and experienced researchers.

Significance. If the review accurately summarizes the literature and the code examples execute correctly, this manuscript provides a useful entry point into Flow Matching, a framework noted for strong empirical results across domains. The explicit code release is a clear strength, supporting reproducibility and lowering barriers to experimentation. No new theoretical claims are advanced, so significance rests on the quality of the exposition and implementation rather than novel results.

minor comments (2)

[Abstract] Abstract: the statement that FM has 'achieved state-of-the-art performance' is presented as background; adding one or two key citations directly in the abstract would help readers locate the supporting empirical papers without searching the main text.
[Code release / examples] The manuscript would benefit from an explicit statement of the PyTorch version and core dependencies used in the released package, ideally in a dedicated 'Reproducibility' subsection or README.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. The review accurately captures the intent of the work as a practical, self-contained resource on Flow Matching.

Circularity Check

0 steps flagged

No significant circularity; review and code guide with no new derivations

full rationale

The manuscript is a self-contained review and tutorial for Flow Matching, summarizing prior mathematical foundations and providing PyTorch examples without advancing any novel theorems, derivations, fitted parameters, or empirical claims. The abstract's SOTA statement is presented as background on existing work rather than a result derived here. No load-bearing steps exist that reduce by construction to self-definitions, fitted inputs renamed as predictions, or self-citation chains, satisfying the criteria for a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper summarizing an existing method, so it does not introduce new free parameters, axioms, or invented entities beyond those already present in the reviewed Flow Matching literature.

pith-pipeline@v0.9.0 · 5404 in / 1113 out tokens · 70865 ms · 2026-05-12T10:22:20.413097+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith.Foundation.DAlembert.Inevitability bilinear_family_forced unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 38 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Generative models on phase space
hep-ph 2026-04 unverdicted novelty 8.0

Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels
cs.LG 2026-05 unverdicted novelty 7.0

Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data
cs.LG 2026-05 unverdicted novelty 7.0

Asymmetric Langevin Unlearning uses public data to suppress unlearning noise costs by O(1/n_pub²), enabling practical mass unlearning with preserved utility under distribution mismatch.
Quantile-Coupled Flow Matching for Distributional Reinforcement Learning
cs.LG 2026-05 conditional novelty 7.0

FlowIQN is a quantile-coupled CFM critic that yields the first explicit Wasserstein-aligned approximate projection for distributional RL, with improved return-distribution accuracy and competitive offline RL performance.
Path-Coupled Bellman Flows for Distributional Reinforcement Learning
cs.LG 2026-05 unverdicted novelty 7.0

Path-Coupled Bellman Flows use source-consistent Bellman-coupled paths and a lambda-parameterized control-variate to learn return distributions via flow matching, improving fidelity and stability over prior DRL approaches.
Mixture Prototype Flow Matching for Open-Set Supervised Anomaly Detection
cs.CV 2026-05 unverdicted novelty 7.0

MPFM uses flow matching with a Gaussian mixture prior on the velocity field and a mutual information maximizer to improve open-set anomaly detection over unimodal prototype methods.
Mixture Prototype Flow Matching for Open-Set Supervised Anomaly Detection
cs.CV 2026-05 unverdicted novelty 7.0

MPFM models flow matching velocity as a Gaussian mixture prior per normal class plus a mutual information regularizer to improve open-set anomaly detection over unimodal prototypes.
Generative Modeling with Orbit-Space Particle Flow Matching
cs.GR 2026-05 unverdicted novelty 7.0

OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
Binomial flows: Denoising and flow matching for discrete ordinal data
cs.LG 2026-05 unverdicted novelty 7.0

Binomial flows close the gap between continuous flow matching and discrete ordinal data by using binomial distributions to enable unified denoising, sampling, and exact likelihoods in diffusion models.
LeapAlign: Post-Training Flow Matching Models at Any Generation Step by Building Two-Step Trajectories
cs.CV 2026-04 unverdicted novelty 7.0

LeapAlign fine-tunes flow matching models by constructing two consecutive leaps that skip multiple ODE steps with randomized timesteps and consistency weighting, enabling stable updates at any generation step.
TokenLight: Precise Lighting Control in Images using Attribute Tokens
cs.CV 2026-04 unverdicted novelty 7.0

TokenLight encodes lighting attributes as tokens in a conditional image generation model trained mostly on synthetic data, enabling precise relighting control and implicit learning of light-scene interactions.
Discrete Flow Matching Policy Optimization
cs.LG 2026-04 unverdicted novelty 7.0

DoMinO reformulates discrete flow matching sampling as an MDP for unbiased RL fine-tuning with new TV regularizers, yielding better enhancer activity and naturalness on DNA design tasks.
TOPOS: High-Fidelity and Efficient Industry-Grade 3D Head Generation
cs.CV 2026-05 unverdicted novelty 6.0

TOPOS creates high-fidelity 3D heads with fixed industry topology from single images via a specialized VAE with Perceiver Resampler and a rectified flow transformer.
Discrete Flow Matching for Offline-to-Online Reinforcement Learning
cs.LG 2026-05 unverdicted novelty 6.0

DRIFT enables stable offline-to-online fine-tuning of CTMC policies in discrete RL via advantage-weighted discrete flow matching, path-space regularization, and candidate-set approximation.
SF-Flow: Sound field magnitude estimation via flow matching guided by sparse measurements
eess.AS 2026-05 unverdicted novelty 6.0

SF-Flow applies flow matching with a permutation-invariant set encoder and 3D U-Net to reconstruct ATF magnitudes from sparse inputs, showing accurate results up to 1 kHz with faster training than autoencoder baselines.
dFlowGRPO: Rate-Aware Policy Optimization for Discrete Flow Models
cs.LG 2026-05 unverdicted novelty 6.0

dFlowGRPO is a new rate-aware RL method for discrete flow models that outperforms prior GRPO approaches on image generation and matches continuous flow models while supporting broad probability paths.
BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation
cs.LG 2026-05 unverdicted novelty 6.0

BRICKS creates compositional neural Markov kernels via hybrid transformers and Riemannian Flow Matching on product manifolds to enable zero-shot simulation of radiation-matter interactions across arbitrary material di...
A Few-Step Generative Model on Cumulative Flow Maps
cs.LG 2026-05 unverdicted novelty 6.0

Cumulative flow maps unify few-step generative modeling for diffusion and flow models via cumulative transport and parameterization with minimal changes to time embeddings and objectives.
Mixture Prototype Flow Matching for Open-Set Supervised Anomaly Detection
cs.CV 2026-05 unverdicted novelty 6.0

MPFM transforms normal features into a structured Gaussian mixture prototype space via a mixture velocity field and mutual information regularization to achieve state-of-the-art open-set supervised anomaly detection.
PRTS: A Primitive Reasoning and Tasking System via Contrastive Representations
cs.AI 2026-04 unverdicted novelty 6.0

PRTS pretrains VLA models with contrastive goal-conditioned RL to embed goal-reachability probabilities from offline data, yielding SOTA results on robotic benchmarks especially for long-horizon and novel instructions.
Learning biophysical models of gene regulation with probability flow matching
q-bio.MN 2026-04 unverdicted novelty 6.0

Probability Flow Matching learns biophysically consistent stochastic processes for gene regulation from time-resolved single-cell measurements, where only the biophysical versions accurately capture lineage transition...
Occupancy Reward Shaping: Improving Credit Assignment for Offline Goal-Conditioned Reinforcement Learning
cs.LG 2026-04 conditional novelty 6.0

Occupancy Reward Shaping extracts goal-reaching rewards from world-model occupancy measures using optimal transport, improving offline goal-conditioned RL performance 2.2x on 13 tasks without changing the optimal policy.
Fisher Decorator: Refining Flow Policy via a Local Transport Map
cs.LG 2026-04 unverdicted novelty 6.0

Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.
Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matching
cs.AI 2026-04 unverdicted novelty 6.0

Mixture-of-experts flow matching enables non-autoregressive language models to achieve autoregressive-level quality in three sampling steps, delivering up to 1000x faster inference than diffusion models.
PhyMix: Towards Physically Consistent Single-Image 3D Indoor Scene Generation with Implicit--Explicit Optimization
cs.CV 2026-04 unverdicted novelty 6.0

PhyMix unifies a new multi-aspect physics evaluator with implicit policy optimization and explicit test-time correction to produce single-image 3D indoor scenes that are both visually faithful and physically plausible.
CellFluxRL: Biologically-Constrained Virtual Cell Modeling via Reinforcement Learning
cs.LG 2026-03 unverdicted novelty 6.0

CellFluxRL post-trains the CellFlux generative model with reinforcement learning driven by biologically meaningful reward functions, yielding virtual cell images that better satisfy physical and biological constraints...
Uncertainty Quantification for Distribution-to-Distribution Flow Matching in Scientific Imaging
cs.LG 2026-03 unverdicted novelty 6.0

Bayesian Stochastic Flow Matching augments flow models with stochastic diffusion for better generalization and uses Monte Carlo Dropout with antithetic sampling to disentangle uncertainties and detect out-of-distribut...
FASTER: Rethinking Real-Time Flow VLAs
cs.RO 2026-03 conditional novelty 6.0

FASTER uses a horizon-aware flow sampling schedule to compress immediate-action denoising to one step, slashing effective reaction latency in real-robot VLA deployments.
Mean Flows for One-step Generative Modeling
cs.LG 2025-05 unverdicted novelty 6.0

MeanFlow uses a derived identity between average and instantaneous velocities to train one-step flow models, achieving FID 3.43 on ImageNet 256x256 with 1-NFE from scratch.
Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching
cs.LG 2026-05 unverdicted novelty 5.0

SharpEuler estimates a sharpness profile via finite differences on calibration trajectories, smooths it, and applies a quantile transform to generate adaptive timestep grids that improve Euler sampling quality in flow...
A Stability Benchmark of Generative Regularizers for Inverse Problems
eess.IV 2026-05 unverdicted novelty 5.0

Numerical benchmarks indicate generative regularizers deliver strong reconstructions in some imaging inverse problem settings but can be unstable or problematic under imperfect conditions compared to variational methods.
Deterministic Decomposition of Stochastic Generative Dynamics
cs.LG 2026-05 unverdicted novelty 5.0

Stochastic generative dynamics admit a transport-osmotic decomposition of the deterministic field, supporting Bridge Matching for interpretable and tunable generation.
Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifolds
cs.LG 2026-04 unverdicted novelty 5.0

Aligning the DDIM forward diffusion process with flow-matching manifold evolution enables high-quality generation without time conditioning, and class-conditional synthesis is possible with an unconditional denoiser b...
Efficient Hierarchical Implicit Flow Q-learning for Offline Goal-conditioned Reinforcement Learning
cs.LG 2026-04 unverdicted novelty 5.0

Proposes mean flow policies and LeJEPA loss to overcome Gaussian policy limits and weak subgoal generation in hierarchical offline GCRL, reporting strong results on OGBench state and pixel tasks.
Exploring Motion-Language Alignment for Text-driven Motion Generation
cs.CV 2026-04 unverdicted novelty 5.0

MLA-Gen advances text-driven motion synthesis by aligning global motion patterns with fine-grained text semantics and mitigating attention sink effects via new masking techniques.
Woosh: A Sound Effects Foundation Model
cs.SD 2026-04 accept novelty 5.0

Woosh is a new publicly released foundation model optimized for high-quality sound effect generation from text or video, showing competitive or better results than open alternatives like Stable Audio Open.
A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
cs.LG 2026-05 unverdicted novelty 4.0

Diffusion, score-based, and flow matching models are unified as instances of learning time-dependent vector fields inducing marginal distributions governed by continuity and Fokker-Planck equations.
Generative models for decision-making under distributional shift
cs.LG 2026-04 unverdicted novelty 3.0

Generative models via pushforward maps, Fokker-Planck equations, and Wasserstein geometry enable learning nominal uncertainty, stressed distributions for robustness, and conditional posteriors under distributional shift.

Reference graph

Works this paper leans on

89 extracted references · 89 canonical work pages · cited by 36 Pith papers · 6 internal anchors

[1]

Building Normalizing Flows with Stochastic Interpolants

Michael S Albergo and Eric Vanden-Eijnden. Building normalizing flows with stochastic interpolants. arXiv preprint arXiv:2209.15571, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[2]

Stochastic interpolants with data-dependent couplings

Michael Samuel Albergo, Mark Goldstein, Nicholas Matthew Boffi, Rajesh Ranganath, and Eric Vanden-Eijnden. Stochastic interpolants with data-dependent couplings. In Proceedings of the 41st International Conference on Machine Learning, ICML'24, 2024

work page 2024
[3]

Transport equation and cauchy problem forbvvector fields

Luigi Ambrosio. Transport equation and cauchy problem forbvvector fields. Inventiones mathematicae, 158 0 (2), 2004

work page 2004
[4]

Reverse-time diffusion equation models

Brian DO Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12 0 (3): 0 313--326, 1982

work page 1982
[5]

Heli Ben-Hamu, Samuel Cohen, Joey Bose, Brandon Amos, Maximillian Nickel, Aditya Grover, Ricky T. Q. Chen, and Yaron Lipman. Matching normalizing flows and probability paths on manifolds. Proceedings of the 39th International Conference on Machine Learning, 162, 2022

work page 2022
[6]

From denoising diffusions to denoising markov models

Joe Benton, Yuyang Shi, Valentin De Bortoli, George Deligiannidis, and Arnaud Doucet. From denoising diffusions to denoising markov models. arXiv preprint arXiv:2211.03595, 2022

work page arXiv 2022
[7]

_0 : Vision-language-action flow model for general robot control

Kevin Black, Noah Brown, Danny Driess, Adnan Esmail, Michael Equi, Chelsea Finn, Niccolo Fusai, Lachy Groom, Karol Hausman, Brian Ichter, Szymon Jakubczak, Tim Jones, Liyiming Ke, Sergey Levine, Adrian Li-Bell, Mohith Mothukuri, Suraj Nair, Karl Pertsch, Lucy Xiaoyang Shi, James Tanner, Quan Vuong, Anna Walling, Haohuan Wang, and Ury Zhilinsky. _0 : Visio...

work page 2024
[8]

Fokker--Planck--Kolmogorov Equations, volume 207

Vladimir I Bogachev, Nicolai V Krylov, Michael R \"o ckner, and Stanislav V Shaposhnikov. Fokker--Planck--Kolmogorov Equations, volume 207. American Mathematical Society, 2022

work page 2022
[9]

Se (3)-stochastic flow matching for protein backbone generation.arXiv preprint arXiv:2310.02391, 2023

Avishek Joey Bose, Tara Akhound-Sadegh, Guillaume Huguet, Kilian Fatras, Jarrid Rector-Brooks, Cheng-Hao Liu, Andrei Cristian Nica, Maksym Korablyov, Michael Bronstein, and Alexander Tong. Se(3)-stochastic flow matching for protein backbone generation. arXiv preprint arXiv:2310.02391, 2023

work page arXiv 2023
[10]

Classifier-free guidance is a predictor-corrector

Arwen Bradley and Preetum Nakkiran. Classifier-free guidance is a predictor-corrector. arXiv preprint arXiv:2408.09000, 2024

work page arXiv 2024
[11]

A continuous time framework for discrete denoising models

Andrew Campbell, Joe Benton, Valentin De Bortoli, Thomas Rainforth, George Deligiannidis, and Arnaud Doucet. A continuous time framework for discrete denoising models. Advances in Neural Information Processing Systems, 35: 0 28266--28279, 2022

work page 2022
[12]

Gener- ative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design.arXiv preprint arXiv:2402.04997, 2024

Andrew Campbell, Jason Yim, Regina Barzilay, Tom Rainforth, and Tommi Jaakkola. Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design. arXiv preprint arXiv:2402.04997, 2024

work page arXiv 2024
[13]

Ricky T. Q. Chen and Yaron Lipman. Flow matching on general geometries. In The Twelfth International Conference on Learning Representations, 2024

work page 2024
[14]

Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. Advances in neural information processing systems, 31, 2018

work page 2018
[15]

What does guidance do? a fine-grained analysis in a simple setting

Muthu Chidambaram, Khashayar Gatmiry, Sitan Chen, Holden Lee, and Jianfeng Lu. What does guidance do? a fine-grained analysis in a simple setting. arXiv preprint arXiv:2409.13074, 2024

work page arXiv 2024
[16]

Theory of ordinary differential equations, 1956

Earl A Coddington, Norman Levinson, and T Teichmann. Theory of ordinary differential equations, 1956

work page 1956
[17]

Sur la forme int \'e gro-diff \'e rentielle des op \'e rateurs de c^ _k dans c satisfaisant au principe du maximum

Philippe Courrege. Sur la forme int \'e gro-diff \'e rentielle des op \'e rateurs de c^ _k dans c satisfaisant au principe du maximum. S \'e minaire Brelot-Choquet-Deny. Th \'e orie du Potentiel , 10 0 (1): 0 1--38, 1965

work page 1965
[18]

Piecewise-deterministic markov processes: A general class of non-diffusion stochastic models

Mark HA Davis. Piecewise-deterministic markov processes: A general class of non-diffusion stochastic models. Journal of the Royal Statistical Society: Series B (Methodological), 46 0 (3): 0 353--376, 1984

work page 1984
[19]

Riemannian score-based generative modelling

Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, and Arnaud Doucet. Riemannian score-based generative modelling. Advances in Neural Information Processing Systems, 35: 0 2406--2422, 2022

work page 2022
[20]

Diffusion models beat gans on image synthesis

Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. In Advances in Neural Information Processing Systems, volume 34, pages 8780--8794. Curran Associates, Inc., 2021

work page 2021
[21]

Guidance: a cheat code for diffusion models, 2022

Sander Dieleman. Guidance: a cheat code for diffusion models, 2022. https://benanne.github.io/2022/05/26/guidance.html

work page 2022
[22]

Ordinary differential equations, transport theory and sobolev spaces

Ronald J DiPerna and Pierre-Louis Lions. Ordinary differential equations, transport theory and sobolev spaces. Inventiones mathematicae, 98 0 (3): 0 511--547, 1989

work page 1989
[23]

Scaling rectified flow transformers for high-resolution image synthesis

Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas M \"u ller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first International Conference on Machine Learning, 2024

work page 2024
[24]

Markov processes: characterization and convergence

Stewart N Ethier and Thomas G Kurtz. Markov processes: characterization and convergence. John Wiley & Sons, 2009

work page 2009
[25]

On second order differential operators

William Feller. On second order differential operators. Annals of Mathematics, 61 0 (1): 0 90--105, 1955

work page 1955
[26]

Existence and uniqueness of martingale solutions for sdes with rough or degenerate coefficients

Alessio Figalli. Existence and uniqueness of martingale solutions for sdes with rough or degenerate coefficients. Journal of Functional Analysis, 254 0 (1): 0 109--153, 2008

work page 2008
[27]

Itai Gat, Tal Remez, Neta Shaul, Felix Kreuk, Ricky T. Q. Chen, Gabriel Synnaeve, Yossi Adi, and Yaron Lipman. Discrete flow matching. arXiv preprint arXiv:2407.15595, 2024

work page arXiv 2024
[28]

Calculus of variations

Izrail Moiseevitch Gelfand, Richard A Silverman, et al. Calculus of variations. Courier Corporation, 2000

work page 2000
[29]

Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud. Ffjord: Free-form continuous dynamics for scalable reversible generative models. arXiv preprint arXiv:1810.01367, 2018

work page Pith review arXiv 2018
[30]

Gradient guidance for diffusion models: An optimization perspective.arXiv preprint arXiv:2404.14743, 2024

Yingqing Guo, Hui Yuan, Yukang Yang, Minshuo Chen, and Mengdi Wang. Gradient guidance for diffusion models: An optimization perspective. arXiv preprint arXiv:2404.14743, 2024

work page arXiv 2024
[31]

Monte carlo sampling methods using markov chains and their applications

W Keith Hastings. Monte carlo sampling methods using markov chains and their applications. 1970

work page 1970
[32]

Iterative -(de) blending: A minimalist deterministic diffusion model

Eric Heitz, Laurent Belcour, and Thomas Chambon. Iterative -(de) blending: A minimalist deterministic diffusion model. In ACM SIGGRAPH 2023 Conference Proceedings, pages 1--8, 2023

work page 2023
[33]

Classifier-free diffusion guidance

Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. In NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021

work page 2021
[34]

Denoising diffusion probabilistic models

Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33: 0 6840--6851, 2020

work page 2020
[35]

Generator matching: Generative modeling with arbitrary markov processes

Peter Holderrieth, Marton Havasi, Jason Yim, Neta Shaul, Itai Gat, Tommi Jaakkola, Brian Karrer, Ricky Chen, and Yaron Lipman. Generator matching: Generative modeling with arbitrary markov processes. Preprint, 2024. http://arxiv.org/abs/2410.20587

work page arXiv 2024
[36]

Riemannian diffusion models

Chin-Wei Huang, Milad Aghajohari, Joey Bose, Prakash Panangaden, and Aaron C Courville. Riemannian diffusion models. Advances in Neural Information Processing Systems, 35: 0 2750--2761, 2022 a

work page 2022
[37]

Riemannian diffusion models

Chin-Wei Huang, Milad Aghajohari, Joey Bose, Prakash Panangaden, and Aaron C Courville. Riemannian diffusion models. In Advances in Neural Information Processing Systems, 2022 b

work page 2022
[38]

Sequence-augmented se (3)-flow matching for conditional protein backbone generation

Guillaume Huguet, James Vuckovic, Kilian Fatras, Eric Thibodeau-Laufer, Pablo Lemos, Riashat Islam, Cheng-Hao Liu, Jarrid Rector-Brooks, Tara Akhound-Sadegh, Michael Bronstein, et al. Sequence-augmented se (3)-flow matching for conditional protein backbone generation. arXiv preprint arXiv:2405.20313, 2024

work page arXiv 2024
[39]

A first course in the numerical analysis of differential equations

Arieh Iserles. A first course in the numerical analysis of differential equations. Cambridge university press, 2009

work page 2009
[40]

Riemannian geometry and geometric analysis, volume 42005

J \"u rgen Jost. Riemannian geometry and geometric analysis, volume 42005. Springer, 2008

work page 2008
[41]

Highly accurate protein structure prediction with alphafold

John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Z \' dek, Anna Potapenko, et al. Highly accurate protein structure prediction with alphafold. nature, 596 0 (7873): 0 583--589, 2021

work page 2021
[42]

Elucidating the design space of diffusion-based generative models

Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in Neural Information Processing Systems, 35: 0 26565--26577, 2022

work page 2022
[43]

Variational diffusion models

Diederik Kingma, Tim Salimans, Ben Poole, and Jonathan Ho. Variational diffusion models. Advances in neural information processing systems, 34: 0 21696--21707, 2021

work page 2021
[44]

Equivalence of stochastic equations and martingale problems

Thomas G Kurtz. Equivalence of stochastic equations and martingale problems. Stochastic analysis 2010, pages 113--130, 2011

work page 2010
[45]

Voicebox: Text-guided multilingual universal speech generation at scale

Matthew Le, Apoorv Vyas, Bowen Shi, Brian Karrer, Leda Sari, Rashel Moritz, Mary Williamson, Vimal Manohar, Yossi Adi, Jay Mahadeokar, et al. Voicebox: Text-guided multilingual universal speech generation at scale. Advances in neural information processing systems, 36, 2024

work page 2024
[46]

Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[47]

Theodorou, Weili Nie, and Anima Anandkumar

Guan-Horng Liu, Arash Vahdat, De-An Huang, Evangelos A. Theodorou, Weili Nie, and Anima Anandkumar. I2sb: image-to-image schr\" o dinger bridge. In Proceedings of the 40th International Conference on Machine Learning, ICML'23. JMLR.org, 2023

work page 2023
[48]

Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[49]

Advanced calculus

Lynn Harold Loomis and Shlomo Sternberg. Advanced calculus. World Scientific, 1968

work page 1968
[50]

Neural manifold ordinary differential equations

Aaron Lou, Derek Lim, Isay Katsman, Leo Huang, Qingxuan Jiang, Ser-Nam Lim, and Christopher De Sa. Neural manifold ordinary differential equations. In Proceedings of the 34th International Conference on Neural Information Processing Systems, 2020

work page 2020
[51]

Scaling riemannian diffusion models

Aaron Lou, Minkai Xu, Adam Farris, and Stefano Ermon. Scaling riemannian diffusion models. Advances in Neural Information Processing Systems, 36: 0 80291--80305, 2023

work page 2023
[52]

48550/arXiv.2401.08740,https://arxiv.org/abs/2401.08740

Nanye Ma, Mark Goldstein, Michael S Albergo, Nicholas M Boffi, Eric Vanden-Eijnden, and Saining Xie. Sit: Exploring flow and diffusion-based generative models with scalable interpolant transformers. arXiv preprint arXiv:2401.08740, 2024

work page arXiv 2024
[53]

Riemannian continuous normalizing flows

Emile Mathieu and Maximilian Nickel. Riemannian continuous normalizing flows. In Advances in Neural Information Processing Systems, 2020

work page 2020
[54]

Vector calculus

Paul C Matthews. Vector calculus. Springer Science & Business Media, 2012

work page 2012
[55]

A convexity principle for interacting gases

Robert J McCann. A convexity principle for interacting gases. Advances in mathematics, 128 0 (1): 0 153--179, 1997

work page 1997
[56]

Action matching: Learning stochastic dynamics from samples

Kirill Neklyudov, Rob Brekelmans, Daniel Severo, and Alireza Makhzani. Action matching: Learning stochastic dynamics from samples. In International conference on machine learning, pages 25858--25889. PMLR, 2023

work page 2023
[57]

Improved denoising diffusion probabilistic models

Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 8162--8171. PMLR, 18--24 Jul 2021

work page 2021
[58]

GLIDE : Towards photorealistic image generation and editing with text-guided diffusion models

Alexander Quinn Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob Mcgrew, Ilya Sutskever, and Mark Chen. GLIDE : Towards photorealistic image generation and editing with text-guided diffusion models. In Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pa...

work page 2022
[59]

Stochastic differential equations

Bernt ksendal. Stochastic differential equations. Springer, 2003

work page 2003
[60]

Semigroups of linear operators and applications to partial differential equations, volume 44

Amnon Pazy. Semigroups of linear operators and applications to partial differential equations, volume 44. Springer Science & Business Media, 2012

work page 2012
[61]

Peluchetti

Stefano Peluchetti. Non-denoising forward-time diffusions. arXiv preprint arXiv:2312.14589, 2023

work page arXiv 2023
[62]

Differential equations and dynamical systems, volume 7

Lawrence Perko. Differential equations and dynamical systems, volume 7. Springer Science & Business Media, 2013

work page 2013
[63]

Computational optimal transport: With applications to data science

Gabriel Peyr \'e , Marco Cuturi, et al. Computational optimal transport: With applications to data science. Foundations and Trends in Machine Learning , 11 0 (5-6): 0 355--607, 2019

work page 2019
[64]

Ashwini Pokle, Matthew J Muckley, Ricky T. Q. Chen, and Brian Karrer. Training-free linear image inversion via flows. arXiv preprint arXiv:2310.04432, 2023

work page arXiv 2023
[65]

Movie Gen: A Cast of Media Foundation Models

Adam Polyak, Amit Zohar, Andrew Brown, Andros Tjandra, Animesh Sinha, Ann Lee, Apoorv Vyas, Bowen Shi, Chih-Yao Ma, Ching-Yao Chuang, David Yan, Dhruv Choudhary, Dingkang Wang, Geet Sethi, Guan Pang, Haoyu Ma, Ishan Misra, Ji Hou, Jialiang Wang, Kiran Jagadeesh, Kunpeng Li, Luxin Zhang, Mannat Singh, Mary Williamson, Matt Le, Matthew Yu, Mitesh Kumar Sing...

work page internal anchor Pith review Pith/arXiv arXiv 2024
[66]

Aram-Alexandre Pooladian, Heli Ben-Hamu, Carles Domingo-Enrich, Brandon Amos, Yaron Lipman, and Ricky T. Q. Chen. Multisample flow matching: Straightening flows with minibatch couplings. In International Conference on Machine Learning, 2023

work page 2023
[67]

Ordinary differential equations and dynamic systems

Jan Pr \"u ss, Mathias Wilke, and Mathias Wilke. Ordinary differential equations and dynamic systems. Springer, 2010

work page 2010
[68]

Exponential convergence of langevin distributions and their discrete approximations

Gareth O Roberts and Richard L Tweedie. Exponential convergence of langevin distributions and their discrete approximations. Bernoulli 2(4): 341-363 (December 1996), 1996

work page 1996
[69]

Diffusions, markov processes, and martingales: Volume 1, foundations

Leonard CG Rogers and David Williams. Diffusions, markov processes, and martingales: Volume 1, foundations. Cambridge university press, 2000

work page 2000
[70]

Moser flow: Divergence-based generative modeling on manifolds

Noam Rozen, Aditya Grover, Maximilian Nickel, and Yaron Lipman. Moser flow: Divergence-based generative modeling on manifolds. Advances in Neural Information Processing Systems, 34: 0 17669--17680, 2021

work page 2021
[71]

Comparison of time-inhomogeneous markov processes

Ludger R \"u schendorf, Alexander Schnurr, and Viktor Wolf. Comparison of time-inhomogeneous markov processes. Advances in Applied Probability, 48 0 (4): 0 1015--1044, 2016

work page 2016
[72]

Palette: Image-to-image diffusion models

Chitwan Saharia, William Chan, Huiwen Chang, Chris Lee, Jonathan Ho, Tim Salimans, David Fleet, and Mohammad Norouzi. Palette: Image-to-image diffusion models. In ACM SIGGRAPH 2022 Conference Proceedings, SIGGRAPH '22. Association for Computing Machinery, 2022

work page 2022
[73]

Progressive Distillation for Fast Sampling of Diffusion Models

Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. arXiv preprint arXiv:2202.00512, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[74]

Applied stochastic differential equations, volume 10

Simo S \"a rkk \"a and Arno Solin. Applied stochastic differential equations, volume 10. Cambridge University Press, 2019

work page 2019
[75]

Neta Shaul, Ricky T. Q. Chen, Maximilian Nickel, Matthew Le, and Yaron Lipman. On kinetic optimal probability paths for generative models. In International Conference on Machine Learning, pages 30883--30907. PMLR, 2023 a

work page 2023
[76]

Neta Shaul, Juan Perez, Ricky T. Q. Chen, Ali Thabet, Albert Pumarola, and Yaron Lipman. Bespoke solvers for generative flow models. arXiv preprint arXiv:2310.19075, 2023 b

work page arXiv 2023
[77]

Neta Shaul, Itai Gat, Marton Havasi, Daniel Severo, Anuroop Sriram, Peter Holderrieth, Brian Karrer, Yaron Lipman, and Ricky T. Q. Chen. Flow matching with general discrete paths: A kinetic-optimal perspective, 2024. https://arxiv.org/abs/2412.03487

work page arXiv 2024
[78]

Diffusion schr\"odinger bridge matching

Yuyang Shi, Valentin De Bortoli, Andrew Campbell, and Arnaud Doucet. Diffusion schr\"odinger bridge matching. In Thirty-seventh Conference on Neural Information Processing Systems, 2023

work page 2023
[79]

Deep unsupervised learning using nonequilibrium thermodynamics

Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learning, pages 2256--2265. PMLR, 2015

work page 2015
[80]

Generative modeling by estimating gradients of the data distribution

Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems, pages 11895--11907, 2019

work page 2019

Showing first 80 references.